Question

How do you graph `tan(x/2)`?

Answer 1

Assuming you know what a tan function looks like, then we know that `y=f(x)`, `f(x)=tanx`

When `y=f(x/a)`, the function is squished along the `x`-axis by `a`. So, `a=` represents all the `x`-values being doubled. So if for a function `f(x)`, `f(2)=5` and `f(4)=12, with`f(x/2)`-`f(4)=5#

So, `y=tan(x/2)` would be `y=tanx` but each value of `x` would be doubled.

`y=tanx`:
graph{tanx [-10, 10, -5, 5]}

`y=tan(x/2)`:
graph{tan(x/2) [-10, 10, -5, 5]}